Practice 4 Solutions

2 2 eat e2t 4 1 1 3 1 11 33 6 find eat where a is

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Unformatted text preview: 3 + e 2t 2 3 3 −1 −1 + e 2t 4 3 −1 −3 1 [4] Find eAt where A is the matrix 3 3 −1 −1 A= λ = 0, 2 eAt = 1 2 −1 −3 1 3 [5] Find eAt where A is the matrix A= λ = −2, 2 eAt = e−2t 4 1 −1 −3 −1 11 33 [6] Find eAt where A is the matrix A= −2 2 −3 3 , 2 × 2 Exercise Set B (distinct roots), November λ = 0, 1 eAt = 3 −2 3 −2 + et −2 2 −3 3 [7] Find eAt where A is the matrix A= λ = −1, 0 2 −2 3 −3 eAt = e−t −2 2 −3 3 + 3 −2 3 −2 e3t 4 1 −1 −3 3 [8] Find eAt where A is the matrix A= λ = −1, 3 eAt = e−t 4 0 −1 −3 2 31 31 + , 2 × 2 Exercise Set C (distinct roots), November 2 × 2 Exercise Set C (distinct roots) Linear Algebra, Dave Bayer, November , [1] Solve the di erential equation y = Ay where 11 , 22 A= λ = 0, 3 eAt = 1 3 2 −1 −2 1 y(0) = e3t 3 + 11 22 1 0 y= 1 3 2 −2 + e3t 3 1 2 [2] Solve the di erential equation y = Ay where A= λ = −2, −1 eAt = e−2t 0 −1 , 2 −3 −1 1 −2 2 y(0) = + e−t 1 2 2 −1 2 −1 1 2 y = e−2t + e−t 0 0 e2t 4 2 −2 [3] Solve the di erential equation y = Ay where A= λ = −2, 2 eAt = e−2t 4 11 33 1 −1 , −3 −1 + e 2t 4 1 1 y(0) = 3 −1 −3 1 y= e−2t 4 2 6 e−3t 3 1 −2 + [4] Solve the di erential equation y = Ay where A= λ = −3, 0 eAt = e−3t 3 −1 1 , 2 −2 1 −1 −2 2 + 1 3 1 0 y(0) = 21 21 y= + 1 3 2 2 [5] Solve the di erential equation y = Ay where A= λ = −1, 2 eAt = e−t 3 11 , 20 1 −1 −2 2 + e 2t 3 y ( 0) = 21 21 1 2 y= e...
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This document was uploaded on 03/24/2014 for the course MATH V2010 at Barnard College.

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